Subcritical Assembly AURES-01 for training purposes; Practical measurements of the effective multiplication factor and the material buckling

AURES-01 is an Algerian subcritical assembly that uses natural uranium as fuel and light water as moderator and neutron reflector, its effective multiplication factor is less than 1. For didactic purposes, such an assembly has certain advantages compared to a critical assembly; It is economical, easy to use, has a lower risk of accidents and low dose rates. This work presents the approach, the method and the results of two experiments, which we realized on the subcritical assembly AURES-01. The first experiment is mainly to determine the effective multiplication factor keff of the subcritical assembly AURES-01. The method consists of gradually charging the medium by fuel elements and carrying out the neutron counting each time. The second experiment, it is to determine the vertical material buckling of subcritical assembly AURES-01. The method is based on measuring the vertical distribution of the neutron flux in different channels. A source of neutrons is used for both experiments.


Introduction
For the purposes of training in the field of nuclear engineering, AURES-01 is a subcritical assembly with fewer risks and constraints than a reactor is widely recommended [1,2,3].
In this framework and to study the physical characteristics of the subcritical assembly AURES-01, two experiments were conducted. The purpose of the first experiment is to determine the effective multiplication factor of the network. The approach consists of gradually loading the medium into fuel elements and counting at each step, the value of the eff k is deduced by extrapolation [1,2,4]. The purpose of the second experiment is to determine the vertical material buckling of the network. The method is based on measuring the vertical distribution of the neutron flux in different channels [1]. The method presented here consists in studying the decay of the neutron population after a source impulse. If a neutron source is induced in a subcritical multiplier medium we will have a flux distribution due to the multiplication of neutrons within this medium. The multiplication rate M is defined as the ratio of the flux density due to fission to that due to the source [1,2,5].
Where I is the average number of counts after each step; 0 I is the number of counts of the neutron source alone. This expression can be written as: Where S is the neutron source term, the expression 2 become: The previous expression is a geometric series whose sum is: Using expression 1, we obtain the expression linking between the multiplication factor and the numbers of counts.

Experimental aspect 2.2.1. Equipment used
In this experience we used the subcritical assembly AURES-01 (figure 1), a Pu-Be (α, n) neutron source, fuel elements made of natural uranium and a neutron measurement system (consisting of a previously calibrated 3 He proportional counter, a preamplifier, a high voltage, an amplifier, an SCA single channel analyzer and a counting scale).
(2) The neutron detector is set to position 2 of the horizontal plane, its vertical position was chosen so as to have a maximum number of counts. (3) The medium is progressively charged with fuel and at each load the counting rate is recorded.

Results
The variation of the multiplication factor eff k as a function of the inverse of the number of fuel elements is given in figure 2. Taking the average value, we obtain the effective multiplication factor of the network AURES-01, eff k =0.8636

Theoretical aspect
The concept of buckling is used to describe the relationship between requirements on fissile material inside a reactor core and dimensions and shape of that core. Geometrical buckling is a measure of neutron leakage, while material buckling is a measure of neutron production minus absorption. With this terminology the criticality condition may also be stated as the material and geometric buckling being equal.
Considering an infinite parallelepiped multiplier (large enough) of dimensions a, b and c containing a point source of neutrons S located in the center that we take as the origin of the coordinates. The parallelepiped material is homogeneous and uniform. If we use the method of diffusion to a group, we obtain the equation of the flux 2 2 0 B ) ) [5][6][7], so: Where 2 B is called material buckling, it describes the characteristics of the fuel material in an infinite medium [4].
Where k f is the infinite neutron multiplication factor, D is the diffusion factor and a 6 is the macroscopic cross section for absorption of the medium.
To determine the value of J we plot the variation of ln ( ) z ) as a function of z . J is the slope of the line found [6,7].

Manipulation
The same equipment as the first experience is used. The procedure of this experiment is as follows: (1) Pu-Be neutron source has been placed in position S (figure 3), this position is considered as origin of the coordinates ( x ; y ; z ), so we have S (0; 0; 0). (2) The first 6 rows were loaded into fuel elements (167 fuel elements in total). Considering the sensitivity of our detector which is 1.8 s , we deduce the neutron flux ) for each count measurement I , so / I s ) [6,7].

Results
The variation of ln ) as a function of the vertical distance z between the source and the detector for the 3 channels (below and above the level of the source) is given in the figures 4 to 6. For each curve the line and the slope were determined.  Taking the average value, we obtain the material buckling for the network of AURES-01: 2 J =0.0018

Conclusion
The value of the eff k found in this work is close to that found previously experimentally [8][9][10], and by theoretical simulation using the WIMS and CITATION and others codes which is about 0.84 [3,8,[10][11][12][13]. The vertical material buckling was determined using three channels so only three horizontal positions ( x , y ), it is recommended to use a higher number of points in order to refine the results. Similarly, for a number of fuel elements.